I'm not sure they're all that comparable... it may be that at 50mm at f/8 you'd find it hard to see much difference. But of course the Sigma has a constant max aperture of f/2.8; the Nikon slower and variable max aperture. The Sigma will provide extra speed if you need to use a faster shutter speed; on the other hand the Nikon has VR and the Sigma doesn't, so it may be a question of whether wider aperture or VR would be more useful to you. The Nikon of course has a much larger zoom range... and for that reason alone I would expect that yes, the Sigma will provide better image quality (to use that fairly broad term) within that range - at least it certainly should if it's anything like the equivalent Tamron.

The Sigma 18-50 f2.8 has average reviews at best. Almost every review I have read has compared it to the Tamron 17-50mm f2.8 and they all say that other than build quality the Tamron wins in every way. Not to mention I think the Tamron is cheaper as well. I will be buying the Tamron in about a month so if you are still looking at that point I will let you know what I think about it. Or you can check out the reviews of both lenses at Popphoto.com

Theoretically, yes. The 3X zoom range of the Sigma is way, way, way easier to correct for a lens designer than the 10X zoom range of the Nikkor. Since I haven't tested either lens, I can't tell you definitively but I would be willing to bet on my theoretical answer.